# If $$\displaystyle{\lim_{x \to \infty}}$$($${x^3+1\over x^2+1}-(ax+b)$$) = 2, then find the value of a and b.

## Solution :

$$\displaystyle{\lim_{x \to \infty}}$$($${x^3+1\over x^2+1}-(ax+b)$$) = 2

$$\implies$$ $$\displaystyle{\lim_{x \to \infty}}$$$$x^3(1-a)-bx^2-ax+(1-b)\over x^2+1$$ = 2

$$\implies$$ $$\displaystyle{\lim_{x \to \infty}}$$$$x(1-a)-b-{a\over x}+{(1-b)\over x^2}\over 1+{1\over x^2}$$ = 2

$$\implies$$ 1 – a = 0, -b = 2 $$\implies$$ a = 1, b = -2

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